Peters had just been flagged for a late hit on Raiders quarterback Derek Carr with 6:05 to play in the second quarter when Penn, left guard Kelechi Osemele and right guard Gabe Jackson went after Peters, prompting Lynch's sprint.
"You know, Marshawn is his cousin, man. They're like brothers," Penn told SportsCenter's Michael Eaves on Friday.
"Marshawn was just trying to get his cousin and make sure his cousin was safe because Marshawn saw three big O-linemen going after his cousin, and Marshawn knows how we get down as offensive linemen. And he knows how his cousin gets down, so I think he was just trying to stop something from getting bigger than it was. He didn't know if a punch was going to get thrown or if it was going to blow up. I think he was just trying to get in there to get his cousin to the sideline, get things safe, get us back playing."
But in rushing to the scrum, Lynch was met by officials, and he responded by bumping line judge Julian Mapp in the chest and then grabbing Mapp by the jersey before letting go.
Lynch was ejected from the game for making contact with an official and then on Friday was suspended one game for his actions. Lynch already has appealed the suspension, a source told ESPN's Adam Schefter.
And while a report surfaced midgame that Lynch left the Coliseum before halftime, he was seen in the stands, watching the game while wearing a mask covering the lower part of his face.
He also was briefly in the Raiders locker room after the game, and videos appeared on social media of him taking BART public transportation home to Oakland and whooping it up with fans, as well as purportedly with Peters, who is also from Oakland.
"I was disappointed that he ran out [on the field] because I knew that we had a 15-yard penalty and we were going to be in good shape," Raiders coach Jack Del Rio said of Lynch after the game.
"I told him, 'You can't leave the bench like that ... ' Obviously, you can never put your hands on an official."
Penn said he spoke with both Lynch and Peters after the game.
"He just got caught up in the moment, trying to protect his cousin," Penn said.
"He's going to learn from it. He was very hard on himself, and he was very down on himself last night."
Penn: 'We knew it was a must-win'
Donald Penn joins SportsCenter to talk about the Raiders' comeback against the Chiefs and Marshawn Lynch's ejection.